ON THE TOTAL INTENSITY OF INTERFERING LIGHT. 229 the integration being extended over the whole aperture. If it should be necessary to suppose a change of phase to take place in the act of diffraction, such change may be included in the constant B. If, then, / be the intensity, n2T /IT . Zirpx + qy 7 7\2 / ff 27rpx+qy7 7 \2 D2/ = sin * , dxdy) + ( cos ^ ^ dxdy} ; \J J A> 0 / \J J A* Q / and if / be the total illumination, -00 ,00 /= Idpdq. J _oo J oo Now, the limits of a?', y7 being the same as those of #, y. Hence, = 1 1 1 / cos TT~ (p^ x + qy' y) dec dy dx dy'. In the present shape of the integral, we must reserve the integration with respect to p and q till the end; but if we introduce the factor e*0^*^, where the sign or -f is supposed to be taken according as p or q is positive or negative, we shall evidently arrive at the same result as before, provided we suppose in the end a and /3 to vanish. When this factor is introduced, we may, if we please, integrate with respect to p and q first. We thus get D2/= limit of 27T j- (px x + qy' y) dec dy dxf dy' dp dq. Now, -oo /"" eTtt-P cos (kp -Q)dp= cos Q eTa^ cos kp dp J -oo J °° 1.00 4- sin Q I e*"P sin ij) dp J -00 f°° . . 2a cos 0 = 2cosQ e-**co*kpdp= ,,.,-.